Question: Calculate the product below and give your answer in scientific notation. $ {\left(800 \right) \times \left(3\times 10^{-1} \right) =\ ?} $
First, let's change the first factor into scientific notation. $(800) \times (3\times 10^{-1}) = (8\times 10^{2}) \times (3\times 10^{-1}) $ Start by collecting the significands and exponents. $ ({8.0} \times {10^{2}}) \times ({3.0} \times {10^{-1}}) = ({8.0} \times {3.0}) \times ({10^{2}} \times {10^{-1}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {24.0} \times {10^{2 \,+\, -1}}$ $= {24.0} \times {10^{1}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${24.0}$ is the same as ${2.40 \times 10}$ or ${2.40 \times 10^{1}}$. $ = {2.40 \times 10^{1}} \times {10^{1}} $ $ = 2.40 \times 10^{{1} + {1}} $ $= 2.40\times 10^{2}$